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 A294243 Sum of the larger parts of the partitions of 2n into two parts with smaller part nonsquarefree. 2
 0, 0, 0, 4, 6, 8, 10, 20, 33, 39, 45, 63, 71, 79, 87, 111, 121, 149, 161, 193, 207, 221, 235, 273, 314, 332, 377, 425, 447, 469, 491, 545, 569, 593, 617, 677, 703, 729, 755, 821, 849, 877, 905, 977, 1052, 1084, 1116, 1196, 1279, 1365, 1403, 1493, 1533, 1627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Index entries for sequences related to partitions FORMULA a(n) = Sum_{i=1..n} (2*n - i) * (1 - mu(i)^2), where mu is the Möbius function (A008683). MAPLE N:= 100: # to get a(1)..a(N) S:= ListTools:-PartialSums(map(t -> `if`(numtheory:-issqrfree(t), [0, 0], [1, t]), [\$1..N])): seq(2*n*S[n, 1]-S[n, 2], n=1..N); # Robert Israel, Oct 27 2017 MATHEMATICA Table[Sum[(2 n - k) (1 - MoebiusMu[k]^2), {k, n}], {n, 80}] Table[Total[Select[IntegerPartitions[2 n, {2}], !SquareFreeQ[#[[2]]]&][[;; , 1]]], {n, 60}] (* Harvey P. Dale, Apr 09 2023 *) PROG (PARI) a(n) = sum(i=1, n, (2*n-i)*(1-moebius(i)^2)); \\ Michel Marcus, Oct 27 2017 CROSSREFS Cf. A008683, A008966, A294244. Sequence in context: A088011 A289424 A050835 * A349694 A298473 A054284 Adjacent sequences: A294240 A294241 A294242 * A294244 A294245 A294246 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Oct 25 2017 STATUS approved

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Last modified June 5 22:25 EDT 2023. Contains 363138 sequences. (Running on oeis4.)